Sensor coil optimization

ABSTRACT

In some embodiments, a coil design system is provided. In particular, a method of providing an optimized position locating sensor coil design in presented. The method includes receiving a coil design; simulating position determination with the coil design to form a simulated performance; comparing the simulated response with the specification to provide a comparison; and modifying the coil design based on a comparison between the simulated performance and a performance specification to arrive at an updated coil design.

RELATED APPLICATIONS

This disclosure claims priority to U.S. Provisional Application62/580,354 filed on Nov. 1, 2017, by inventors QAMA and SPECOGNAentitled “Sensor Coil Optimization,” which is herein incorporated byreference in its entirety.

TECHNICAL FIELD

Embodiments of the present invention are related to position sensorsand, in particular, to optimization of the sensor coils in a positionsensor.

DISCUSSION OF RELATED ART

Position sensors are used in various settings for measuring the positionof one component with respect to another. Inductive position sensors canbe used in automotive, industrial and consumer applications for absoluterotary and linear motion sensing. In many inductive positioning sensingsystems, a transmit coil is used to induce eddy currents in a metallictarget that is sliding or rotating above a set of receiver coils.Receiver coils receive the magnetic field generated from eddy currentsand the transmit coils and provide signals to a processor. The processoruses the signals from the receiver coils to determine the position ofthe metallic target above the set of coils. The processor, transmitter,and receiver coils may all be formed on a printed circuit board (PCB).

However, these systems exhibit inaccuracies for many reasons. Forexample, the electromagnetic field generated by the transmitter, and theresulting fields generated in the metallic target, may be non-uniform,the connections of wire traces to the transmit coils and the arrangementof receive coils may result in further non-uniformity. The air-gap (AG)between the metallic target and the coils mounted on the PCB may benon-uniform. Further, the amplitudes of signals generated by receivercoils may have an offset. There may be mismatches between the multiplereceiver coils. There may be different coupling effects between themetallic target and each of the multiple receiver coils. These and otherfactors may result in inaccurate results of the position locatingsystem.

Therefore, there is a need to develop better methods of designing sensorcoils that offer better accuracy for position sensing.

SUMMARY

In some embodiments, a coil design system is provided. In particular, amethod of providing an optimized position locating sensor coil design inpresented. The method includes receiving a coil design; simulatingposition determination with the coil design to form a simulatedperformance; comparing the simulated response with the specification toprovide a comparison; and modifying the coil design based on acomparison between the simulated performance and a performancespecification to arrive at an updated coil design.

These and other embodiments are discussed below with respect to thefollowing figures.

BRIEF DESCRIPTION OF THE FIGURES

FIGS. 1A and 1B illustrates a coil system for determining a position ofa target.

FIGS. 2A, 2B, 2C, 2D, and 2E illustrate response of the receiver coilswhile sweeping a metallic target across the coil system.

FIGS. 3A and 3B illustrate configuration of receive coils on a printedcircuit board in a coil system.

FIG. 3C illustrates inhomogeneity of electromagnetic fields generated bya transmit coil in the coil system.

FIGS. 3D and 3E illustrate discrepancies in fields measured by receivercoils in a coil system.

FIG. 4A illustrates a block diagram of a testing device that tests theaccuracy of a position locate system.

FIG. 4B illustrates a test device such as that illustrated in FIG. 4A.

FIG. 4C illustrates testing a position locating system with the testdevice illustrated in FIG. 4B.

FIG. 4D illustrates received voltages from receive coils in the positionlocating system measured with the test device illustrated in FIG. 4B.

FIG. 5 illustrates a measured response and a simulated response.

FIG. 6 illustrates an error between the measured and simulated responsesof an example coil design optimized according to embodiments of thepresent invention.

FIG. 7A and 7B illustrate an algorithm for optimizing coil design for aposition location sensor according to some embodiments of the presentinvention.

FIG. 7C illustrates an input screen shot for a system operating thealgorithm illustrated in FIG. 7A.

FIGS. 8A and 8B illustrate a coil design according to some embodimentsof the present invention

FIGS. 9A, 9B, and 9C illustrate another example coil design according tosome embodiments of the present invention.

FIGS. 9D and 9E illustrate performance characteristics of a coil designaccording to some embodiments.

FIG. 10A illustrates a simulation algorithm according to someembodiments.

FIGS. 10B and 10C illustrate the fields generated around a wire and thefields generated around a rectangular trace.

FIGS. 10D and 10E illustrate an error generated by treating arectangular trace as a one-dimensional wire, multi-wires, or 3D bricks.

FIG. 10F illustrates a simulation of eddy currents in a metallic targetover receiver coils.

FIG. 11 illustrates an algorithm for adjusting the receiver coil designaccording to some embodiments.

FIG. 12 illustrates another embodiment of an algorithm for adjusting thereceiver coil design according to some embodiments.

FIG. 13 illustrates optimizing a design without wells.

FIG. 14 illustrates an optimized design with wells.

These and other aspects of embodiments of the present invention arefurther discussed below.

DETAILED DESCRIPTION

In the following description, specific details are set forth describingsome embodiments of the present invention. It will be apparent, however,to one skilled in the art that some embodiments may be practiced withoutsome or all of these specific details. The specific embodimentsdisclosed herein are meant to be illustrative but not limiting. Oneskilled in the art may realize other elements that, although notspecifically described here, are within the scope and the spirit of thisdisclosure.

This description illustrates inventive aspects and embodiments shouldnot be taken as limiting—the claims define the protected invention.Various changes may be made without departing from the spirit and scopeof this description and the claims. In some instances, well-knownstructures and techniques have not been shown or described in detail inorder not to obscure the invention.

FIG. 1A illustrates a positioning system 100. As illustrated in FIG. 1A,the positioning system includes transmit/receive control circuit 102that is coupled to drive a transmitter coil 106 and receive signals fromreceive coils 104. In most configurations, receive coils 104 are locatedwithin transmitter coil 106, however in FIG. 1A they are illustratedseparately for clarification purposes. Receive coils 104 are generallyphysically located within the border of transmit coil 106.

Embodiments of the present invention can include a transmitter coil 106,two receiver coils 104, and an integrated circuit (IC) 102 driving thetransmitter coil 106 and measuring the signals originated in thereceiver coils 104 all formed on a printed circuit board (PCB).

FIG. 1B illustrates a configuration of transmit coils 106 and receivecoils 104 in a linear position locating system. As is shown in FIG. 1B,a conductive metallic target 124 can be positioned over the transmittercoil and the two receiver coils.

As is illustrated in FIG. 1A, transmit coil 106 is driven to formmagnetic field 108. Transmit coil 106 can be driven at a range offrequencies or at particular frequencies. In FIG. 1A, magnetic field108, with the positive current illustrated by the arrows, is circulararound each wire and in a direction that points out of the page insidecoil 106 and into the page outside of coil 108 with the currentdirection as illustrated in FIG. 1A. Receive coils 104 are locatedinside coil 106, as is illustrated in FIG. 1B. Transmit coil 106 isdriven at any frequency that can produce electromagnetic field 108 toinduce voltages in receiver coils 104. In general, there can be anynumber of receiver coils, however, for ease of discussion, a system withtwo receiver coils is discussed below.

FIG. 1B illustrates the arrangement of sensor receive coils (RX) 104within transmit coil (TX) 106. As illustrated in FIG. 1B, sensor receivecoils 104 includes a sine wave oriented coil RXSIN 112 and a cosineoriented signal coil RXCOS 110. Sine wave oriented coil RXSIN 112includes sine loops 114, 116, and 118 where coil 112 is wound inin-phase or anti-phase directions, here depicted as clockwise or counterclockwise depictions, to result in the production of voltages in theloop of opposite sign as a result of the presence of electro-magneticfield 108. As is illustrated, the wiring of sine wave oriented coil 112provides a clockwise rotation in loops 114 and 118 resulting in anominally positive voltage and a counterclockwise rotation in loop 116resulting in nominally negative voltages. Similarly, cosine orientedcoil 110 may include a first loop 120 with a clockwise orientation and asecond loop 122 with a counterclockwise orientation FIG. 1B illustratesa possible electromotive force reference direction, as indicated by thearrows, that is consistent with the magnetic fields produced bytransmitter coil 106 as illustrated in FIG. 1A. As one skilled in theart will recognize, the orientations may be interpreted otherwise.

In the system illustrated in FIG. 1B, the transmitter coil (TX) 106 isstimulated by the circuit 102, which may be an integrated circuit, togenerate a variable Electromagnetic field (EMF), illustrated as EMFfield 108. The magnetic field 108 couples with the receiver coils (RX)104. If a conductive metallic target 124 is placed on the top of thereceiver coils 104 as illustrated in FIG. 1B, an eddy current isgenerated in the metallic target 124. This eddy current generates a newelectromagnetic field that is ideally equal and opposite of field 108,canceling the field in receiver coils 104 directly under metallic target124. The receiver coils (RX) 104 capture the variable EMF field 108generated by the transmit coils 106 and those induced by metallic target124, resulting in sinusoidal voltages generated at the terminals ofreceiver coils 104.

In absence of metallic target 124, there will be no voltage at theterminals of the RX coils 104 (labeled RxCOS 110 and RXSin 112 in FIG.1B). When metallic target 124 is placed in a specific position withrespect to the RX coils 104, the resultant electromagnetic field on thearea covered by the metallic target 124 is ideally zero and thereforethe voltages at the terminals of the RX coils 104 will have differentcharacteristic depending on the location of metallic target 124 relativeto receiver coils 104. The RX coils 104 are designed in a way that asine voltage is created at the terminals of one RX coil (RxSin 112) anda cosine voltage is created at the terminals of the other RX coil (RxCos110) as metallic target 124 is swept across receiver coils 104. Theposition of the target with respect to the RX coils 104 modulates theamplitude and the phase of the voltage at the terminals of the RX coils104.

As illustrated in FIG. 1A and discussed above, transmitter coil 106,receive coils 104, and transmit/receive circuit 102 can be mounted on asingle PCB. Further, the PCB can be positioned such that metallic target124 is positioned above receive coils 104 and spaced from receive coils104 by a particular spacing, the air gap (AG). The position of metallictarget 124 relative to the PCB on which receive coils 104 andtransmitter coil 106 is mounted can be determined by processing thesignals generated by sine oriented coil 112 and cosine oriented coil110. Below, the determination of the position of metallic target 124with respect to receive coils 104 is described in a theoretical idealcondition.

In FIG. 1B, metallic target 124 is located at a first location. In thisexample, FIG. 1B and FIGS. 2A, 2B, and 2C depict operation of a linearposition locator system. The principle of operation is the same in bothlinear and circular locators. In the discussion below, the position isgiven in relation to the construction of cosine oriented coil 110 andsine oriented coil 112 by providing the angular relations with respectto the sine operation of sine oriented coil 112 which results from theposition of the leading edge of metallic target 124 and coils 110 and112. The actual position of metallic target 124 in such a system can bederived from the angular position as measured by the output voltages ofreceive coils 104 and the topology of receive coils 110 and 112.Furthermore, as illustrated in FIG. 1B, the topology of coil 110 and thetopology of coil 112 are coordinated to provide indication of thelocation of metallic target 124.

FIG. 2A illustrates the 0° position of metallic target 124 with cosineoriented coil 110 and sine oriented coil 112 separated for ease ofexplanation. As shown in FIG. 1B, sine oriented coil 112 and cosineoriented coil 110 are co-located within transmit coil 106. Using themagnetic field 108 as illustrated in FIG. 1A, loops 114, 116, and 118 ofsine oriented coil 112 are positioned such that the sum of the voltagesin each loop cancels so that the total V_(sin) is 0. As illustrated inFIG. 2A, in the absence of metallic target 124, the voltage in loop 114,V_(c) can be represented as ½, the voltage in loop 116 (because thecurrent in that loop is opposite the current in loops 114 and 118) canbe represented as V_(d)=−1, and the voltage in loop 118 can berepresented as V_(e)=1/2. Consequently, the voltage in coil 112 isV_(sin)=V_(c)+V_(d)+V_(e)=0. Consequently, if metallic target 124 is notpresent, then the output signal from sine oriented coil 112 would be 0.

Similarly, if metallic target 124 is not present, then the output signalfrom cosine oriented loop 110 is also 0 because the voltage generated bymagnetic field 108 in loop 120, V_(a)=−1 cancels the voltage generatedby magnetic field 108 in loop 122, V_(b)=1, so thatV_(cos)=V_(a)+V_(b)=0. As discussed above, the voltage depictionsprovided here are proportional and depicted as a proportion of a fullloop—loops 120, 122, and 116 can have a maximum representation of 1while loops 114 and 118 can have a maximum representation of½. The signrepresents the reference direction of the loop, which results ingeneration of the voltage from that loop. The reference direction isarbitrary and consistent results can be calculated regardless of whichof the two possible directions is chosen to depict positive.

However, with metallic target 124 placed at the 0° position, themagnetic field 108 in loop 114 of sine oriented coil 112 is canceled byeddy currents generated in metallic target 124 so that V_(c)=0. In loop116 of sine oriented coil 112, the magnetic field 108 in the half ofloop 116 under metallic target 124 is canceled by eddy currents formedin metallic target 124, but a voltage is generated by the magnetic field108 in the half of loop 116 that does not lie under metallic target 124.Since half of loop 116 is exposed, the voltage generated is V_(d)=−1/2.Further, voltage is generated in loop 118 of sine oriented coil 112 suchthat V_(e) is ½. However, the voltage generated by loop 116 is canceledby the voltage generated in loop 118, resulting in the voltage signalacross sine oriented loop 112 is 0; V_(sin)=V_(c)+V_(d)+V_(e)=0.

In the same orientation of metallic target 124 with respect to cosineoriented coil 110, loop 120 is covered by metallic target 124 so thatV_(a)=0. Loop 122 is exposed so that V_(b)=1. Therefore, the voltageacross cosine oriented coil 110, V_(cos), is given by V_(a)+V_(b)=1.

FIG. 2B illustrates metallic target 124 in a 90° position with respectto sine oriented coil 112 and cosine oriented coil 110. As illustratedin FIG. 2B, in sine oriented coil 112, metallic target 124 coverscompletely loop 116 and leaves loops 114 and 118 uncovered. As aconsequence, V_(c)=½, V_(d)=0, and V_(e)=½ so thatV_(sin)=V_(c)+V_(d)+V_(e)=1. Similarly, in cosine oriented coil 110,half of loop 120 is covered resulting in V_(a)=−1/2 and half of loop 122is covered resulting in V_(b)=½. Consequently, V_(cos), given byV_(a)+V_(b), is 0.

Similarly, FIG. 2C illustrates metallic target 124 in a 180° positionwith respect to sine oriented coil 112 and cosine oriented coil 110.Consequently, half of loop 116 and loop 118 in sine oriented coil 112are covered by metallic target 124 and loop 122 in cosine oriented loop110 is covered by metallic target 124. Therefore V_(a)=−1, V_(b)=0,V_(c)=1/2, V_(d)=−1/2, and V_(e)=0. As a result, V_(sin)=0 andV_(cos)=−1.

FIG. 2D illustrates a graph of V_(cos) and V_(sin) versus angularposition of metallic target 124 with the coil topology provided in FIGS.2A, 2B, and 2C. As is illustrated in FIG. 2D, the angular position canbe determined by processing the values of V_(cos) and V_(sin). Asillustrated by sweeping the target from a defined initial position to adefined end position, in the output of the receivers will be generated asinusoidal (Vsin) and cosinusoidal (Vcos) voltage illustrated in FIG.2D.

The angular position of metallic target 124 relative to receive coils104 can be determined from the values of Vsin from sine oriented coil112 and Vcos cosine oriented coil 110 as is illustrated in FIG. 2E. Forexample, the angular position of the target can be calculated as

Angular position=arctan (Vsin/Vcos).

FIG. 2E illustrates this and shows the sinusoidal forms of V_(cos) andV_(sin) along with the determination of the position of metallic target124 derived from the values of V_(cos) and V_(sin). In a linear positionlocating system, the linear position can be determined by the angularposition through knowledge of the wavelength of the sinusoidal forms ofthe traces of receiver coils 104 (i.e., the separation between peakseparation areas of the traces of the sine oriented coil 112 and thecosine oriented coil 110). In an angular position locating system, thesine oriented coil 112 and cosine oriented coil 110 can be arranged suchthat the angular position can be equal to the actual angular position ofthe metallic target 124 with respect to the rotation of metallic target124.

It is important to note the following conditions that indicate an idealoperation of position location sensor 100. Among those conditions arethat the shape of transmitter coil 106 has no importance as long as itcovers the area where the receiver coils 104 are placed. Further, theshape of the receiver coils 104 is equal to a perfect geometricaloverlapped sine and cosine. Additionally, the shape of metallic target124 has no influence on the working principle as long as the area of thetarget covers a part of the total area of the receiver coils 104.

These conditions for an ideal set of coils and ideal metallic target arenever met. In a real system, the situation is very different. Thenon-ideality leads to inaccuracy in the determination of the position ofmetallic target 124. Among the issues that result in inaccuracies inlocation determination include non-uniformity of the electromagneticfield generated in transmit coil 106; connections of metallic tracesbetween transmit/receive circuit 102 and receive coils 104 andconnections of metallic traces between transmit/receive circuit 102 andtransmit coil 106, which also contribute to the generatedelectromagnetic fields; the air gap (AG) between metallic target 124 andthe PCB on which receive coils 104 and transmit coil 106 is mounted;amplitude offsets between sine oriented coils 112 and cosine orientedcoils 110; mismatches between signals from receive sine oriented coils112 and cosine oriented coils 110; different coupling effects in sineoriented coils 112 and cosine oriented coils 110. Further, there is astrong correlation between the air gap (AG) between the metallic target124 and the PCB and the accuracy of the location determination.Furthermore, in the ideal world, the topology of sine oriented coil 112and cosine oriented coil 110 are ideal trigonometric functions but in anactual design these coils 104 are not ideal and have several throughvias to allow traces to be intertwined on the PCB by using both sides ofthe PCB.

FIG. 3A illustrates a sine oriented coil 112 oriented on a PCB (notshown in FIG. 3A for clarity). The PCB is positioned such that tracesthat form sine oriented coil 112 are positioned on a top side and abottom side of the PCB. In this disclosure, references to the top sideor the bottom side of the PCB indicated opposite side of the PCB andhave no other meaning regarding the orientation of the PCB. In general,the position locating system is oriented such that the top side of thePCB faces a surface of metallic target 124. FIG. 3B illustrates a topside of PCB 322 on which top side traces for formation of transmit coil106, sine oriented receiver coil 112, and cosine oriented receiver coil110 are formed.

As is illustrated in FIG. 3A, coil 112 is formed by traces 302 on thetop side of the PCB 322 and traces 304 on the bottom side of the PCB322. Traces 302 and 304 are electrically joined by vias 306 formedthrough the PCB 322. As is illustrated in FIG. 3A, vias 306, top sidetraces 302, and bottom side traces 304 are arranged to allow formationof cosine oriented coil 112. For example, portions 310 and 312 allow forcrossing of coil 112 to form loops 114, 116, and 118 while separated thetraces at the intersection. As is further illustrated, portions 314,316, 318, and 320 allow for overlay of cosine oriented coil 112 on thePCB.

However, vias 306 and the existence of traces 302 and 304 on oppositesides of PCB 322 decrease the effective amplitude of the signal detectedby coils 104. Effectively, vias 306 make the gap distance betweentransmit coil 106 and signal coils 104, which has a large influence initself on accuracy of the position locating system. This is combinedwith the increase in the effective air gap between metallic target 124and signal coils 104 on the PCB 322 due to traces of signal coils 104being formed both on the top side and the bottom side of PCB 322.

FIG. 3B illustrates a further problem with symmetries where transmitcoil 106 is not symmetric with receive coils 104. In the case shown inFIG. 3B, receive coils 104 are not centered on the transmit coils 106and the traces that form connections to receive coils 104 and totransmit coil 106 are also not symmetric.

FIG. 3C illustrates the non-uniformity of the magnetic field strengthgenerated by transmit coils 106. As is illustrated in FIG. 3C, twotraces of transmit coil 106 are located at positions 0 and 5 on thegraph while receive coils 104 are positioned between positions 0 and 5.FIG. 3C illustrates the magnetic field between these traces has aminimum between the two traces. FIG. 3C does not illustrate the furtherdistortion because of the two traces that connect the two tracesillustrated in FIG. 3C and run perpendicular to the traces illustratedin FIG. 3C.

FIGS. 3D and FIG. 3E further illustrates inaccuracies that can resultfrom displacements in transmit coil 106. As illustrated in FIGS. 3D and3E, transmit coil 106 includes a displacement 330 that distorts themagnetic field produced by transmit coil 106. Stray fields fromdisplacement 330 produce imbalances in the receive coils 104.Consequently, inaccuracies in position determination will develop fromsuch features.

FIGS. 4A and 4B illustrate a calibration and test device 400 that can beused to evaluate position locating systems. Due to non-idealities of themagnetic coupling principle such as those described above, a calibrationprocedure can be used to correct the measured position of the targetwith respect to the positioning device. Furthermore, system 400 can beused to test the accuracy of positioning systems such as those describedabove.

FIG. 4A illustrates a block diagram of an example system 400. As isillustrated in FIG. 4A, a metallic target 408 is mounted on a platform406 such that is over a position locating system 410. A positioner 404is capable of moving platform 406 relative to position locating system410 in a precise manner. As discussed above, position locating system410 includes transmit coils and receive coils formed on a PCB and mayinclude a controller 402 that receives and processes signals from thereceive coils and drives the transmit coil.

As is further shown in FIG. 4A, metallic target 408 is positioning in az-direction to provide an air gap (AG) between metallic target 408 andposition locating system 410. In some embodiments, positioner 404 iscapable of moving metallic target 408 linearly in an x-y plane asillustrated in coordinate system 420. In some embodiments, positioner404 rotates metallic target 408 around a center-of-rotation overposition locator system 410 as needed, for example, for testing arotation locator rather than a linear locator.

Controller 402 is coupled to provide control signals and receive thereceive coil signals from positioner 404. Controller 402 is furthercoupled to provide transmit power to transmit coils on locating system410 and to receive and process signals from receive coils in locatingsystem 410. As illustrated above, position locating system 410 mayinclude a transmit coil 106, cosine oriented coil 110, and sine orientedcoil 112 as discussed above. In some cases, controller 402 may bemounted on the same PCB with transmit coil 106, cosine oriented coil110, and sine oriented coil 112 of locating system 410 and providelocate signals to a separate processor 422.

Processor 422 can be any processing system capable of interfacing tocontroller 402 and to positioner 404. As such, processor 422 may includeone or more microcomputers, transient and nontransient memory, andinterfaces. Processor 404 communicates with positioner to determine theprecise location of metallic target 408 with respect to positionlocating system 410 and to provide signals to positioner 404 thatdetermine the sweep of metallic target 408 over the receive coilsmounted in position locating system 410. As such, processing unit 422can compare the measured position of metallic target 408 as determinedby controller 402 with the determined position as provided by positioner404 to evaluate the accuracy of position locating system 410. In someembodiments, controller 402 may be combined with processing unit 422,which performs all of the tasks for determining the actual position ofmetallic target 408 from positioner 404 and the measured position ofmetallic target 408 from coils on position locating system 410 anddetermining the accuracy of the measured position from position locatingsystem 410.

As is further illustrated in FIG. 4A, controller 402 can include aprocessor 412 (which may a processor in processor 422) that drives thetransmit coils and receives signals from the receive coils as well asprocesses the data from the receive coils in order to determine thelocation of metallic target 508 relative to the receive coils. Processor412 can, through interface 424, communicate with devices such asprocessing unit 422. Further, processor 412 drives a transmit coil suchas transmit coil 106 through a driver 404. Driver 404 may includecircuitry such as digital-to-analog converters and amplifiers to providecurrent to transmit coils such as transmit coil 106. Additionally,processor 412 can receive the receive signals Vsin and Vcos from receivecoils such as coils 110 and 112. The signals Vsin and Vcos from thereceive coils is received into buffers 416 and 418, which may includecircuitry such as filters and amplifiers as well as analog-to-digitalconverters to provide digital data to processor 412. Processor 412 cancalculate a position as described above to provide positional data ofmetallic target 408 with respect to the receive coils on positionlocating system 410.

FIG. 4B illustrates an example of positioning system 400. Positioner 404is coupled to a mount 406 and can include four stepper motors thatprovide a 4-axis movement of the target—x, y, z and rotational aroundthe z axis. As such, system 400 as illustrated in FIG. 4B is able tosweep the metallic target 408 on the top of the receiver coils inposition locator system 410 in all possible directions, including the zdirection to create different air gaps. As discussed before, the air gapis the distance between the metallic target 408 and the PCB where thetransmit and receive coils of position locate system 410 are placed.Such a system can be used for calibration, linearization, and analyzingthe accuracy of position locator system 410.

FIG. 4C illustrates a sweep of a metallic target 408 over a rotationposition locator system 410 with transmit coils 106 and receive coils104. As is illustrated in FIG. 4C, metallic target 408 is swept from 0°to θ° over receiver coils 104. FIG. 4D illustrates an example of thevoltages Vsin and Vcos measured from receiver coils 104 compared withthe results of the simulation as metallic target 408 is swept asillustrated in FIG. 4C. In the particular example of FIG. 4D, metallictarget 408 is swept in 50 positions. The crosses represent the samplevoltages and the continuous lines represents values simulated by anelectromagnetic field solver program, CDICE-BIM.

The accuracy of position locator system 410 can be defined as thedifference between the measurement of the position during a sweep of themetallic target 408 from an initial position to an end position and anexpected ideal curve for that sweep. This result is expressed inpercentage respect to the full scale, as is illustrated in FIG. 5. InFIG. 5, Pos0 is the measured value from position locating system 410 andthe output-fit is the ideal curve.

${FNL} = \frac{100\left( {{{Pos}\; 0} - {Ideal}_{curve}} \right)}{Fs}$

Pos0 is the value measured from a register of controller 402 while FS isthe value at full scale. For example, with a 16 bit register FS is2E16−1=65535. FIG. 6 illustrates the error in terms of FNL % FS asdetermined by the above equation. The goal is to produce positionsensing with the best possible accuracy, for example of 0.2% FS or less.

If the coil design on a PCB is designed using a trial and error method,the best achieved accuracy is 2.5% FS -3% FS. In a sensor formed on aPCB there are two receiver coils and one transmitter coil. The accuracyof the position measured is extremely relevant to the coil design. Trialand error coil design on PCB have empirically attempted to resolvesthese issues. However, such a simplified and inaccurate method can onlytake into account a limited set of the issues. All these procedures donot lead to a successful design because the whole system,coil—target—traces, is more complex than can be easily accounted for andthe optimal solution has to take into account a more substantial numberof the parameters if the resulting coil design will meet desiredaccuracy specifications.

FIG. 7A illustrates an algorithm 700 for providing a coil design on aprinted circuit board for an accurate position locating system accordingto some embodiments of the present invention. Algorithm 700 can beexecuted on a computing system with sufficient computing power toexecute the appropriate simulations. Such a system would typicallyinclude a processor coupled to memory. The memory may include bothvolatile and non-volatile memory for storage of data and programming. Insome cases, fixed storage such as hard drives and such can be utilized.The system would include user interfaces such as keyboards,touchscreens, video displays, pointing devices, or other commoncomponents. The system would be capable of executing the algorithmsdescribed here, interacting with a user, and outputting a finalized coildesign for production of a printed circuit board with the optimizeddesign.

As illustrated in FIG. 7A, algorithm 700 starts with an input step 702.In step 702, a first coil design is input for optimization. Inparticular, the coordinates, layout, and characteristics of the transmitcoil and the receive coils are entered, including information regardingconnection nodes, vias, and other parameters regarding these coils.Additionally, the design of the metallic target, including the air gapdistance between the metallic target and the coils, is input. Further,the desired specification for the accuracy of the position locationsystem that results is provided. System operating parameters (e.g., thefrequency and strength at which transmit coils are expected to bedriven) are also input. Once the data is input to algorithm 700 in step702, algorithm 700 continues to step 704. FIG. 7C illustrates ascreen-shot indicating input of coil design parameters of step 702.

In step 704, the response to the input of power to the transmit coilwith the metallic target at various position through its sweep issimulated. In particular, the fields generated by the metallic target inresponse to the fields generated by the transmit coil is determined.From those fields, the response of the receive coils for the currentcoil design is simulated. From the receive coil response, a position ofthe metallic target calculated from the receive coil response iscompared with the position of the metallic target as set during thesimulation.

In step 706, the simulated position is compared to the set positionposition of the metallic target. In step 708, if the specification ismet, algorithm 700 proceeds to step 710 where the final optimized coildesign is output. In step 708, if the specification is not met algorithm700 proceeds to step 712.

In step 712, the design of the coils on the PCB are adjusted inaccordance with simulated results from step 704 and the comparison instep 706 in order to improve the accuracy of the finally designed coildesign. In some embodiment, the transmitter coil design remains fixed asinput into step 702 and the receiver coil design and layout are adjustedto improve accuracy. In some embodiments, the transmitter coil may alsobe adjusted to improve accuracy.

Algorithm 700 shown in FIG. 7A results in a coil design for printing ona printed circuit board with a simulated accuracy as specified duringthe specification input that occurred in step 702. FIG. 7B illustratesan algorithm 720 for verifying a coil design, which may be the coildesign produced by algorithm 700 in FIG. 7A.

As shown in FIG. 7B, a coil design is input in step 722. The coil designmay be an older legacy design, may be a new design, or may have beenproduced by algorithm 700 as illustrated in FIG. 7A. In step 724, asimulation is performed on the coil design. In some cases, where thecoil design input is produced by algorithm 700, this simulation hasalready been performed in step 704 of algorithm 700. Otherwise, asimilar simulation is performed. In step 726, the coil design isphysically produced on a printed circuit board. In step 728, thephysically produced coil design response is measured, for example withpositioning system 400 as illustrated in FIGS. 4A and 4B.

In step 730, the measured results from the physically produced coildesign are compared with the simulated results from the coil design.Step 730 may, then, validate the simulation performed in step 724 withrespect to its accuracy. In step 732, if the simulation matches themeasured results, then algorithm 720 proceeds to step 734 where the coildesign has been validated. In step 732, if the simulated results do notmatch the physically measured results, then algorithm 720 proceeds tostep 736.

In step 736, if algorithm 720 is being performed as a validation of acoil design produced by algorithm 700, the input design to algorithm 700is modified and algorithm 700 rerun. In some embodiments, in step 736 anerror is produced indicating that the simulation is not operatingproperly and therefore the simulation itself need adjusting in order tobetter simulate all of the non-idealities in the particular positionlocating system. In that case, step 736 can also be a model calibrationalgorithm.

Consequently, in some embodiments of the present invention, an optimizedcoil design can be produced by iteratively providing a simulation of thecurrent coil design and then modifying the coil design according to thesimulation until the coil design meets specifications as desired. Insome cases, as a final step, the optimized coil design is physicallyproduced and tested to insure that the simulation matches the physicallymeasured properties. This procedure can help to optimize the coildesign, whether the goal is to optimize and redesign an old coil designon PCB or whether the goal is to design and optimize a new coil designon PCB.

An existing coil design on a PCB can be validated according to algorithm720 and potentially improved according to algorithm 700. The existingcoil design can be extracted, for example, in a Gerber format usingelectronic design automation (EDA) or computer-aided design (CAD)systems. In some embodiments, inputs of the initial coil design in step702 of Algorithm 700 or step 722 in algorithm 720 can be performed inthe Gerber format. The output design in step 710 can also be in theGerber format. Gerber formatting is commonly used in CAD/CAM systems andthe such for representing printed circuit board design and can beobtained from Ucamco USA, San Francisco, Calif.

As such, an existing design can be extracted from the existing printedcircuit board and provided to algorithm 720 in step 722 for validationor to algorithm 700 in step 702. As such, as described above, theperformance of the existing design can be performed in step 724 and theactual performance measured in step 728. The simulated and measuredresponses can be compared in step 730 and the system validated in step732.

As discussed above, measuring the response in step 728 can includesweeping the metallic target from a start point to an end point withconstant air gap. The simulation can be run with the same PCB designwith the same Air Gap and with the same target. This process, called avalidation processes, is important to understand if the simulation isperforming correctly and the simulation reflects all the non-idealitypresent in the design.

Once the capability to simulate correctly the coils on the PCB has beenvalidated, then existing design can be input to step 702 of algorithm700 and modified in a way to improve the accuracy, for example theoffset and nonlinearity, of the resulting position locating system. Thisapproach can be accomplished automatically in the iterative algorithmillustrated by steps 704, 706, 708 and 712 of FIG. 7A and uses asimulation code in step 704 and a coil design code in step 712 toconverge on an optimum design. The improved Design Coil, which is outputin step 710, can then be printed on a PCB with the help of an EDA Tool.

A completely new design can be implemented in much the same way that anexisting design can be implemented. In particular, the new design can beinput to step 702 of algorithm 700 and algorithm 700 can be executed tooptimize the coil design. The optimized coil design output in step 710of algorithm 700 can then be input to algorithm 720 and the designactually produced for testing. Algorithm 720 can then validate operationof the optimized coil design, as discussed above

The coil design tool executed in step 712 of algorithm 700 can be usedto design the geometrical shape of the sine and cosine on a PCB usingthe coil design tool of step 712 in accordance with the simulationsperformed by simulation tools in step 704. The iterative algorithm foroptimizing the coil design, as illustrated in algorithm 700, includesthe simulation tool in step 704 and the coil design tool of step 712. Inparticular, algorithm 700 calculates the minimum position error in step706 and minimizes non idealities of the Rx Coils in steps 706, 708 and712. With the coordinates obtained after this optimization, PCB can beprinted using a commercial EDA tool as in step 710.

Embodiments of the invention can be used to produce coil designs forposition locating systems for all the applications that need positionsensor technology, torque, torque angle sensors (TAS) and every otherapplication that uses inductive principle and receiver coils on a PCB.The benefits of certain embodiments include having zero offset on bothreceivers, which means achieving the theoretic limit that is zero.Achieving 0.5% FS error from a starting point of 2.5% FS-3% FS thatoccurred before the optimized Coil (an improvement of a factor of 6) canbe achieved. Further, no linearization or calibration method is neededif the error is reduced well enough. Additionally, the number of trialsand errors used to produce a viable coil design can be reduced,providing for a shortened product introduction and time to market.

FIGS. 8A and 8B illustrate an example of a coil layout 800 on a PCB (notshown for clarity) that can be used as an input to algorithm 700 asillustrated in FIG. 7A. In some cases, the optimized coil designresulting from algorithm 720 will be modified by algorithm 700 in orderto optimize the accuracy of coil layout 800. FIG. 8A illustrates coillayout 800 while FIG. 8B illustrates a planar view of coil layout 800,which overlaps the traces on the top side and the bottom side of thePCB.

As is illustrated in FIGS. 8A and 8B, coil design 800 includestransmission coil 802, which may include multiple loops and may furtherinclude vias through the PCB so that some of the traces for transmissioncoil 802 is on one side of the PCB while other traces of transmissioncoil 802 are on the opposite side of the PCB. In some cases, thetransmission coil can be optimized to render it as symmetric withrespect to the receive coils as possible while minimizing the requiredspace. FIG. 8A illustrates vias 814 and 816 which allow the traces oftransmission coil 802 to be connected between sides of the PCB. As isfurther illustrated in FIGS. 8A and 8B, receive coils include cosineoriented coils 804 and sine oriented coils 806. Cosine oriented coils804 include vias 818 that allow transition of the wire traces of cosineoriented coils 804 from one side of the PCB to the other. Similarly,sine oriented coils 806 include vias 820 that allow for transition ofwiring for sine oriented coils 806 between sides of the PCB.

Another feature that is included in coil layout 800 are the addition ofwells 808, 810, and 812 that compensate further for non-uniformity ofthe fields generated by transmit coils 802 and a resulting offset errorgenerated by that non-uniformity. As is illustrated in coil design 800,well 808 and 810 are provided to adjust sine oriented coil 804 and well812 is set to adjust cosine oriented coil 806. Further, vias 822 and 824can be provided so that the traces of wells 808 and 812, respectively,can be on either side of the PCB. Wells 808, 810, and 812 can, forexample, compensate for offsets in receive coils 804 and 806 due tonon-uniformity in the fields generated by transmit coils 802.

FIGS. 9A, 9B, and 9C illustrate another coil design according to someembodiments of the present invention. As opposed to the linear positionsystem illustrated in coil design 800, coil design 900 illustrated inFIGS. 9A, 9B, and 9C illustrate a rotary position system. As shown incoil design 900, transmission coil 902, cosine oriented receive coil 904and sine oriented receiver coil 906 are oriented in a circular fashion.Further, transmission coil 902 includes a distortion portion 916 withleads 920. Sine oriented receiver coil 906 includes wells 908 and 912and is connected to a lead 924. Similarly, cosine oriented receiver coil904 includes wells 910 and 914 and is coupled to lead 926. The PCB mayalso have mounting holes 918. FIG. 9A illustrates a planar view of coildesign 900 while FIG. 9B illustrates an angled view of coil design 900that illustrates vias and traces on both sides of a PCB board on whichit is formed. FIG. 9C illustrates a plan view of coil design 900 on aprinted circuit board 930. Further, a control circuitry 932, coupled toleads 920, 924, and 926, mounted on circuit board 930.

FIG. 9D illustrates the percentage error between the actual positionlike the one used in positioning system 400, and the positionreconstructed by the simulation by using the RX voltages in, forexample, step 704 of algorithm 700. As illustrated in FIG. 9D, thepercentage error between theoretical and simulated results, after coildesign 900 has been optimized according to algorithm 700, is less than0.7%. FIG. 9E illustrates the actual angular position versus thesimulated angular position after coil design 900 has been optimizedaccording to algorithm 700. FIG. 6 illustrates again the percentage ofFull Scale error for the optimized coil design 900 after a linearizationalgorithm has been applied. On that scale, the error is less than 0.3%FS.

Embodiments of the invention include a simulation step 704 thatsimulates the response of a position locating system coil design and acoil design adjustment algorithm 712 that, using the simulated response,adjusts the coil design for better accuracy. As is discussed above,position sensors suffer from a number of non-idealities. First of all,the field produced by the TX coils is highly non-uniform and because ofthis non-uniformity the gap between the target and the RX coils allows alot of magnetic flux not to be correctly shielded by the target. Anothereffect is that the parts of the RX coils on the bottom of the PCBcapture less induced magnetic flux than the corresponding parts in thetop of the PCB. Finally, the exits of the RX coils that allow aconnection with the controller chip also produce an offset error whichis sensible. In the linear and arc sensors, there is additionally thestrong effect of the ends of the sensor which produce a huge strayfield. This last effect is responsible for most error on the linear andarc designs.

As discussed above, optimization of the coil design begins with a goodsimulation in step 704 of algorithm 700. In a first iteration,simulation is performed on the initial coil design input in step 702 ofalgorithm 700. In accordance with some embodiments, simulation includesan eddy current solver algorithm developed at the University of Udine,Italy. In particular, an example of a simulation algorithm uses aBoundary Integral Method (BIM), introduced in the publication P.Bettini, R. Specognz, “A boundary integral method for computing eddycurrents in thin conductors for arbitrary topology,” IEEE Transactionson Magnetics, Vo. 41, No. 3, 7203904, 2015, which provides a very fastsimulation (a couple of tens of seconds for 25 target positions). Suchan algorithm can be tailored for simulating traces on PCBs and inductivesensor applications. In particular, the simulation can input thegeometry of the PCB traces, the geometry of the metallic target, the airgap, the translation/rotation of the metallic target over the coilsformed by the traces, and additional fixed conductors that, for example,can be used to simulate ground planes of the PCT or other conductorsnearby the sensor. The simulation can output the simulated voltages fromreceiver coils at a series of positions of the metallic target over thecoils.

In some embodiments, a Finite Element Method (FEM) or analogous methodmay also be used in this application. However, in some cases largeamounts of computing time may be needed to perform these simulations. Itwould be expected that the calculations for each sensor target positionmay use two or more orders of magnitude of computational time withrespect to the BIM method described above. Further, the mesh of thecomputation domain may need to be rebuilt from scratch for each targetposition. Furthermore, accuracy in these techniques may be limited sincelong and thin conductors require a lot of mesh elements to obtain anaccurate solution. These calculations may also be limited by memory andcomputing time resources.

FIG. 10A illustrates an example of simulation step 704 of algorithm 700.Algorithm 700 as illustrated in the example of FIG. 7A, in effect,substantially compensates for the non-ideal effects described above andproduces, therefore, the best possible solutions compatible with thephysics of the problem of providing an accurate position locationsystem. To accomplish this, a realistic and efficient numerical model ofthe position locating system is developed. As discussed in more detailbelow, in some embodiments traces that form transmit coils, receivercoils, and connecting lines are represented with one-dimensionalmetallic wires. Some embodiments may use more refined simulationalgorithms, for example such as brick volumetric elements, partialelements equivalent circuit (PEEC), or an approach based on volumeintegral formulations, which may provide further enhancement toestimating the magnetic field produced by actual three dimensionalcurrent carrying structures. The metallic target can usually berepresented by a conducting surface.

As is illustrated in FIG. 10A, algorithm 704 begins at step 1002. Instep 1002, the PCB trace design that describes the TX coil and the RXcoils, the geometry of the target, the air gap specifications, and thesweep specification is obtained. These input parameters, for example,can be provided by algorithm 700, either through the initial inputduring input step 702 of algorithm 700 or from the adjusted coil designfrom coil adjustment step 712 of algorithm 700, as is illustrated inFIG. 7A. Algorithm 704 then proceeds to step 1003.

In step 1003, algorithm 704 computes the resistance R and inductance Lof the traces of the transmission coil (TX) at the frequency parameterset in step 1002. The computation is performed without the presence ofthe target to give an estimation of the quality factor Q=2πfL/R.

In step 1004, parameters are set to simulate the performance of aparticular coil design and air gap of the coil design received in step1002 with the metallic target set at a present position as defined inthe sweep parameters. If this is the first iteration, the presentposition is set at the beginning of the sweep defined in the datareceived in step 1002. Otherwise, the position is set at the currentlydefined position in the sweep.

In step 1006, the electromagnetic fields generated by the transmissioncoils are determined. The driving voltages and operating frequency forthe transmission coils are received with the other parameters providedin step 1002.

Once the electromagnetic fields from the transmission coil isdetermined, in step 1008 the eddy currents generated in the metallictarget as a result of those fields can be determined. From the eddycurrents, the fields generated by the target can be simulated.

In step 1010, the voltages generated in the receiver coils due to thecombination of the fields generated by the transmission coil and thefields generated by the induced eddy currents in the metallic target aredetermined. In step 1011 the computation of the inductance L isperformed again for the present position of the target to evaluate thevariation of L with respect to the result of step 1003. In step 1012,the response data is stored for future reference.

In step 1014, algorithm 704 checks to see if the sweep has beencompleted. If not, then algorithm 704 proceeds to step 1018 where thecurrent position of the metallic target is incremented and then to step1004 where the simulation with that position is started. If the sweep iscompleted, algorithm 704 proceeds to step 1016 where the simulation endsand the algorithm returns to step 706 of algorithm 700 illustrated inFIG. 7A.

Simulations and reconfiguration of the coils according to thesimulations (in FIG. 7A, simulation step 704, comparison step 706,decision step 708, and design adjustment step 712) should be fast enoughto test a large number of coil design configurations in a short periodof time. Hundreds, or even thousands, of simulations may be used beforean optimized coil design is achieved by algorithm 700. Consequently,there are some model simplifications that, although not substantiallyaffecting the accuracy of the simulation, can substantially increase thespeed. If each simulation takes 10 seconds to complete, for example, anoptimization that uses 100 iterations may take 16 minutes. If eachsimulation takes 10 minutes to complete, however, that same optimizationmay take 16 hours to complete.

An effective simplification used in some embodiments is to represent theconducting traces used in formation of transmit coils and receiver coilswith a one-dimensional wire model. In a worst-case deviation from aone-dimensional wire model, consider a benchmark rectangular trace witha height of 35 μm and a width of 0.3 mm. The rectangular trace can beformed of any non-magnetic conductive material, for example copper.Other metals may be used to form traces, but copper is more typical. Thecurrent density of current flowing within the rectangular trace can bevery uniform for a section of the trace with thickness on the order oftwice the skin depth. For copper, the skin depth is 30 μm at a frequencyof 5 MHz. Consequently, for the benchmark rectangular trace discussedabove, the current density within the trace will be substantiallyuniform.

FIG. 10B illustrates the field generated by a current carryingone-dimensional wire 1020. There is no difference in the field generatedby wire 1020 or by a straight cylinder of a diameter, if the currentflowing in the two structures is the same. FIG. 10C, however,illustrates the field generated around benchmark trace 1022, which isthe benchmark trace described above formed of copper and with height of35 μm and width of 0.3 mm. As is illustrated in FIG. 10C, the field evenat short distances of less than 1 mm looks the same as that generated bywire 1020 in FIG. 10B. The difference is in the fields less than about 1mm from the trace.

FIG. 10D illustrates the difference between a one-dimensional model ofwire 1020 and the benchmark rectangular trace 1022 at a distance of 1 mmfrom the center of the trace. The representation of a singularrectangular trace 1022 can be realized both with a single-wire and amulti-wire configuration. As can be seen, the field deviates slightlyfrom the one-dimensional model. As can be seen from FIG. 10D, the erroris not negligible, but in both cases it is a small fraction of 1% evenat 1 mm. Since most points of the receive coils are much further than 1mm away with respect to transmission coils, the 1d-wire model maysuffice in most applications.

It is also possible to represent the transmission coil withthree-dimensional brick shaped elements in which the current density isassumed to be uniform. FIG. 10E illustrates this approximation. As isillustrated in FIG. 10E, this reduces the modeling error of the magneticfield produced by the transmission coil by one order of magnitude at amodest additional computational price.

Consequently, in step 1006 and in step 1010, the traces can be modeledas one-dimensional traces. The source magnetic field produced by thetransmit coil is therefore pre-computed by using the 1d-wire model. Insome embodiments, more advanced models based on 3D brick elements, whichas discussed above can produce roughly the same results, can be used.These models may use a finite-element-matrix form of computations,however such models may need many elements and require a significantincrease in computation. As discussed above, FEM-like models may use toomany elements (100+millions mesh elements) to reach the precision of theproposed one-dimensional model.

FIG. 10F illustrates positioning of a metallic target 1204 over receivercoils 1028 and 1026 in a position location system design that is beingsimulated in algorithm 704. For purposes of discussion, FIG. 10Fillustrates an example of coil design 800 illustrated in FIGS. 8A and8B, with receiver coils 1028 and 1026 corresponding with theone-dimensional approximation to the traces of receiver coils 804 and806, respectively. Transmit coil 802 is not illustrated in FIG. 10F forsimplification of the illustration, but the traces of transmit coil 802is also approximated by one-dimensional wire traces.

After the electromagnetic fields from the target coil 802 of theposition locating system 800 have been simulated, then in step 1008 ofthe example of algorithm 704 illustrated in FIG. 10A, the eddy currentsof the metallic target 1024 are simulated and the electromagnetic fieldsthat result from those eddy currents are determined. The induced eddycurrents in metallic target 1024, in some embodiments, are computed byan original Boundary Integral Formulation.

Metallic target 1024 can typically be modeled as a thin metal sheet.Usually, metallic target 1024 is thin, 35 μm to 70 μm, while the lateraldimensions are typically measured in millimeters. As discussed abovewith respect to wire traces, when conductors have a thickness less thanabout twice the penetration depth of the magnetic field at a particularoperating frequency, the induced current density is substantiallyuniform across the layer thickness. Therefore, the thin conductor ofmetallic target 1024 can be modeled as a surface in which the inducededdy currents are tangent to the surface. If this is not the case, themore computationally expensive Volumetric Integral Formulations like,the one provided in P. Bettini, M. Passarotto, R. Specogna, “A volumeintegral formulation for solving eddy current problems on polyhedralmesses,” IEEE Transactions on Magnetics, Vol. 53, No. 6, 7204904, 2017,or Finite Element modeling can be used to model the target.

As is further illustrated in FIG. 10F, the surface of metallic target1024 is represented as covered by mesh elements 1026. Mesh elements 1026are non-overlapping polygons, typically triangular, that cover theentire surface of metallic target 1024 and form a discrete surface.

Once the simulation on metallic target 1024 is performed in step 1008 of704, as illustrated in FIG. 10A, then in step 1010 the response ofreceiver coils 804 and 806 is simulated. As is further illustrated inalgorithm 704, simulation 704 sweeps the target across position locatorsystem 800 and estimates “in silico” the voltages on the receive coils804 and 806 for all specified positions of the target 1024.

As is further illustrated in step 712 of algorithm 700 illustrated inFIG. 7A, the shape of receive coils 804 and 806, assuming that transmitcoil is adapted in the best possible way to all non-idealities of thesensor 800 at the same time. This represents the best solution, giventhat the non-idealities cannot be all removed and as discussed aboveseveral approximations are used in simulation algorithm 704.

FIG. 11 illustrates an example of algorithm 712. In algorithm 712, thecenterline of the receive coils 804 and 806 traces and transmit coil 802are represented as one-dimensional pathways. Splines or any otherinterpolation function can be used to link the one-dimensional pathwaysto form the shape of transmit coil 802 and receive coils 804 and 806.More efficiently, the distortion of the receive coils may be realized bythe application of a suitable function. For example, in the rotarysensor the function will be a function of the radius.

In step 1102, the current coil design layout, the simulation results,and in some cases the comparison provided in step 706 are input andreceived in algorithm 712. A non-linear programming solver can then beused to find the shape of transmit coil 802 and receive coils 804 and806 that minimize a given objective function. The objective function isformed by three parts as illustrated in FIG. 11. In step 1103 the widthof the external wells 1402 and 1404 illustrated in FIG. 14 isestablished in order to minimize the offset without the target. In step1104, the root mean square of error (RMS) between the detected position(i.e. the electrical angle) and the ideal one is minimized. This doesnot impose anything about the shape of the voltage V_(cos) and V_(sin)with respect to position. In step 1106, algorithm 712 evaluates the RMSof the difference between two sinusoids with equal amplitude and thesimulated values of Vcos and Vsin as a function of position in order toconstrain the shape of the output voltages. In some embodiments, theshape of the redesigned receive coils 804 and 806 may converge in bothsteps 1104 and 1106.

In some embodiments, steps 1104 and 1106 may use Metaheuristicoptimization solvers. Metaheuristic optimization solvers tend to be veryslow, however. Therefore, in some embodiments metaheuristic globalsearching technique like genetic algorithms or particle swarm algorithmscan be used. In some embodiments, a deterministic algorithm like theinterior point method or the trust region algorithm can be used in steps1104 and 1106. In particular, since initial starting designs for receivecoils 804 and 806 can be standard sine and cosine profiles, and theresulting optimized design should result in a small perturbation of theinitial design, then it is expected that local search methods can beused to sufficiently find the global minima resulting in optimaldesigns. The basics of optimization theory can be found, for example, inS. S. Rao, Engineering Optimization: Theory and Practice, John Wiley &Sons, 2009.

FIGS. 12 illustrates another embodiment of algorithm 712. The inputprovided in step 1202 is the same as that discussed with respect to step1102 of FIG. 11. In step 1204, the transmission coil (TX) isautomatically generated providing the maximum symmetry and reducing thespace required.

An example transmission coil that can result is shown in FIG. 13 wherethe trace deviation 1304 is computed according to the PCB specificationsin term of trace to trace distance and vias dimensions (pad radius).Moreover, a reduction of the space can be obtained with the alternatevias positioning 1302.

In the embodiment of algorithm 712 illustrated in FIG. 12, the algorithmadjusts the sine receive coil and the cosine receive coil is definedrelative to the modified sine receive coil. One skilled in the art willrecognize that instead of modifying the sine receive coil, the cosinereceive coil could be modified instead and the sine receive coil definedrelative to the cosine receive coil. For illustrative purposes, FIG. 13illustrates the modification of a sine receive coil as described withrespect to FIG. 12.

Receiving coils (RX) design can be defined with a double loop iteration.Initially, in step 1206, the sine shaped RX coil 1316 is symmetricallypartially extended along x direction (with the reference system 1314) asin trace 1310 to compensate the flux leakage due to the targetnon-idealities. With the imposed coil extension, in step 1208 the sineshaped coil 1316 is then deformed along y direction as in trace 1312using a proper displacement function acting on all the points of thecoil 1316. Given these settings, in step 1210 the algorithm computes theposition of the vias. The vias position 1308 is established accordingwith information specified in step 1202 and in order to eliminate thesignal mismatch previously mentioned. Voltage mismatch appears wheneverthere are more vias in one receiver coil than there are in the otherreceiver coil or the vias are positioned in an unbalanced way (i.e. notsymmetric). The voltage mismatch that results is a greater peak-to-peakamplitude of the sine signal with respect to the cosine signal (or viceversa) when the target is moving. To achieve the goal of reducingvoltage mismatch, the vias are designed in such a way that the length ofthe parts of the SIN (1316) and COS (1318) RX coils in the bottom of thePCB is the same. Moreover, the vias are symmetric with respect to thesymmetry center of the design.

In step 1212, the sine and cosine receive coil traces are defined. Insome embodiments, a one-dimensional model is used to define the traces.

In step 1214, algorithm 712 computes the offset without the target andin step 1216 if the minimum offset criterion is not satisfied thealgorithm restarts from step 1208. When the minimum offset is reachedthe algorithm proceeds to step 1218, evaluating the voltages asdescribed in FIG. 10A and then computing the maximum error between theideal and the simulated positions. If the lowest possible error is notreached in step 1220, the algorithm goes back to step 1206 providinganother configuration. Once the lowest error for the current input isobtained the algorithm ends at return step 1226.

In some embodiments the offset without target compensation is realizedwithout the presence of the wells as illustrated in FIG. 13. Anyway, thedesign symmetry is always guaranteed thanks to the balanced extensions1306 and 1307 of the sine shaped 1316 and cosine shaped 1318 RX coils.

The above detailed description is provided to illustrate specificembodiments of the present invention and is not intended to be limiting.Numerous variations and modifications within the scope of the presentinvention are possible. The present invention is set forth in thefollowing claims.

1. A method of providing an optimized position locating sensor coildesign, comprising: receiving into a computing system a coil design anda performance specification, the coil design being represented in adatafile to provide transmit coil, sine coil, and cosine coilcoordinates; simulating, in the computing system, position determinationover a range of positions of a metallic target with respect to the coildesign to form a simulated performance of the coil design, the simulatedperformance representing the simulated response of the sine coil andcosine coil to the metal target excited by the transmit coil over therange of positions; comparing, in the computer system, the simulatedresponse with the performance specification to provide a comparison;modifying, in the computer system, the coil design based on thecomparison between the simulated performance and the performancespecification to arrive at an updated coil design that more performsaccording to the performance specification; and providing the updatedcoil design.
 2. The method of claim 1, further including repeating thesimulating, comparing, and modifying steps on the updated coil designsto arrive at a final coil design with optimized performance that meetsthe performance specification; and providing the final design forprinting on a printed circuit board.
 3. The method of claim 1, whereinthe coil design and the updated coil design includes a transmit coillayout, a sine receive coil layout, a cosine receive coil layout, ametallic target geometry, a sweep geometry, and an air gap.
 4. Themethod of claim 3, wherein simulating position determination includes,for each of a set of positions within the range of positions of ametallic target over the coil design, computing parameters for thetransmit coil in the absence of the sine receive coil and the cosinereceive coil; determining an electromagnetic field produced by thetransmit coil; determining eddy currents induced in the metallic targetby the electromagnetic field produced by the transmit coil at a presentlocation from the set of positions of the target; determining a responseof the sine receiver coil and the cosine receiver coil produced by theeddy currents in the metallic target; computing a second set ofparameters for the transmit coil with the metallic target; and storingthe voltage signals as a function of the position of the metallictarget.
 5. The method of claim 3, wherein each of the receive coilsincludes one or more wells.
 6. The method of claim 3, wherein traces ofthe transmit coil and traces of the receive coils are treated asone-dimensional wires.
 7. The method of claim 4, wherein determiningeddy currents includes simulating the metallic target with aboundary-integral-method.
 8. The method of claim 1, further including:physically producing a position locating system according to the finaldesign; and validating the position locating system against simulatedresults of the stored voltage signals.
 9. The method of claim 3, whereinmodifying the coil design comprises: establishing well amplitude for thesine receive coil and the cosine receive coil; minimizing a root meansquare (RMS) error between a simulated position and an ideal position;evaluating a root mean square distance between sinusoids and thesimulated cosine and sine voltages; and providing the updated coildesign.
 10. The method of claim 9, minimizing the RMS error and the RMSdistance is accomplished with a metaheuristic optimization solver. 11.The method of claim 3, wherein modifying the coil design comprises:generating a symmetric transmit coil layout with minimum space;extending a receive coil according to a boundary flux leakage; settingthe receive coil amplitude according to an offset; calculating symmetricvia positions that avoids a voltage mismatch; defining coil traces forthe receive coil and a second receive coil; and calculating an offsetwithout the presence of the target.
 12. The method of claim 11, furtherincluding checking minimum offset criteria; and modifying the amplitudeof the receive coil if the minimum is not met.
 13. The method of claim12, further including if the minimum offset criteria is met, evaluatingthe maximum error and modifying the receive coil design if the lowestcriteria is not met.
 14. A position sensor, comprising: a transmit coilwith minimum space; a sine receive coil positioned with respect to thetransmit coil, the sine receive coil including vias and a well; a cosinereceive coil positioned with respect to the transmit coil and the sinereceive coil, the cosine receive coil including vias and a well; and ametallic target positioned over the transmit coil, the sine receivecoil, and the cosine receive coil, wherein the position sensor has beenoptimized with respect to providing position accuracy.